Pseudospectral bound and transition threshold for the 3D Kolmogorov flow

Abstract

In this paper, we establish the pseudospectral bound for the linearized operator of the Navier-Stokes equations around the 3D Kolmogorov flow. Using the pseudospectral bound and the wave operator method introduced in [LWZ], we prove the sharp enhanced dissipation rate for the linearized Navier-Stokes equations. As an application, we prove that if the initial velocity satisfies $\Vert U_0-(k_f^{-2}\sin (k_{f}y),0,0){\Vert }_{H^2}\le c{\nu }^{\frac{7}{4}}$ ($\nu$ the viscosity coefficient) and $k_f\in (0,1)$, then the solution does not transition away from the Kolmogorov flow.

66 pages

References in corpus (2)

• Pseudospectral and spectral bounds for the Oseen vortices operator
• Stability of the Couette flow at high Reynolds number in 2D and 3D